Position, navigation, and timing (PNT) systems operate by estimating parameters such as time-of-arrival (TOA) and direction-of-arrival (DOA) of received signals. Such parameters can be estimated using cross-correlation between separate signals. For instance, the global maximum of a cross-correlation function of two signals substantially similar in shape can be indicative of the relative time delay between the two signals. Also, for multipath signals, local maxima of the cross-correlation function can be indicative of secondary communication paths.
The use of correlation functions between signals to estimate signal parameters can suffer accuracy degradation especially when the signals are associated with a relatively smooth autocorrelation function or multipaths that are not far enough apart. For instance, for a relatively smooth autocorrelation function, errors in localizing respective peaks can increase due to noise, channel distortion, or computational errors. Time localization of sharp peaks can be more robust in the presence of noise, or other distortion factors. Furthermore, multipaths that are separated by short relative time delays translate into peaks that are close to one another in the correlation function. The proximity of such peaks makes it difficult to reliably and accurately distinguish between them.
Methods using correlation functions can be, in some cases, computationally costly. The computation of a correlation function involves a larger number of multiplications. The number of multiplications increases as the number of samples in the correlated signals increase. In particular, while correlation methods perform better with wideband signals, the computational complexity for such signals can be relatively high, for example, compared to narrow band signals.